Chapter 4: Fundamentals of Quantum Mechanics

Question 1

transverse wave characteristics (4)

Answer 1

• amplitude is the difference between the midpoint and the trough
• wavelength is the length of one complete cycle of a wave, described as the difference between consecutive crest or toughs
• the frequency of a wave is the number of complete cycles of the wave that transmit per unit time, or how “frequent” the particles in the wave vibrate as a result of the wave passing through
• intensity and energy of a wave are proportional to the square of its amplitude

Question 2

standing waves

Answer 2

• bound on either side and do not carry energy from one location to another

Question 3

constant c

Answer 3

• speed of light in a vacuum

Question 4

nodes (2)

Answer 4

• points in standing waves where the oscillation amplitude is zero
• attachments or endpoints are not considered to be nodes

Question 5

Heisenberg uncertainty principle

Answer 5

• one cannot know precisely (with zero uncertainty) both the position and momentum of a microscopic particle at the same time

Question 6

states (2)

Answer 6

• represented by different n values, n values are positive integers
• n values encodes or labels the state of the particle

Question 7

phase

Answer 7

• represents the sign for the wavefunction and it is always alternating

Question 8

what does the square of the wavefunction give?

Answer 8

• probability distribution for the system, it is always positive

Question 9

why is the energy quantized

Answer 9

• energy depends on n and since n values are restricted to positive integers the energy of a particle in a box can only have certain, specific values

Question 10

ground state

Answer 10

• state given by n=1

Question 11

excited state

Answer 11

• when the particle has an energy higher than the ground state energy

Question 12

zero-point energy

Answer 12

• difference between the ground state energy and zero

Question 13

what does quantization arise from?

Answer 13

• it arises from confinement, thus the energy of a particle in a one-dimensional box is quantized (can only take on certain values)

Question 14

what is the energy of a particle in a one-dimensional box dependent on?

Answer 14

• the integer number n, the mass m, and the size of the box L

Question 15

what are the wavefunction and energy states labelled by?

Answer 15

• quantum numbers, which for the particle in a box are positive integers (n=1, 2, 3….)

Question 16

what does the lowest energy possible in a one-dimensional box correspond to?

Answer 16

• to the ground state, n=1

Question 17

how many nodes do the wave function and probability distribution have?

Answer 17

• each have n-1 nodes

Question 18

total energy equation with momentum and mass

Answer 18

E = p^2/2m

Question 19

wavefunction formula

Answer 19

• ψ(x) = sqaureroot(2/L) sin(nπx/L)

Question 20

energy equation using h, n, m, and L

Answer 20

E = h^2*n^2/8mL^2

Question 21

wavelength formula

Answer 21

• 2L/n